OFFSET
1,2
COMMENTS
Terms from 11 to 117 are the atomic numbers of the elements in group 17 in the periodic table. The elements in this group are also called halogens.
LINKS
Colin Barker, Table of n, a(n) for n = 1..1000
Index entries for linear recurrences with constant coefficients, signature (2,1,-4,1,2,-1).
FORMULA
From Colin Barker, Nov 14 2017: (Start)
G.f.: x*(1 + 9*x - 6*x^2 - 6*x^3 + 9*x^4 - x^5 - 4*x^6 + 2*x^7) / ((1 - x)^4*(1 + x)^2).
a(n) = (1/12)*(2*n^3 + 12*n^2 + 28*n - 12) for n>2 and even.
a(n) = (1/12)*(2*n^3 + 12*n^2 + 22*n - 24) for n>2 and odd.
a(n) = 2*a(n-1) + a(n-2) - 4*a(n-3) + a(n-4) + 2*a(n-5) - a(n-6) for n>8.
(End)
MATHEMATICA
LinearRecurrence[{2, 1, -4, 1, 2, -1}, {1, 11, 17, 35, 53, 85, 117, 167}, 50] (* Paolo Xausa, Oct 21 2024 *)
PROG
(PARI) Vec(x*(1 + 9*x - 6*x^2 - 6*x^3 + 9*x^4 - x^5 - 4*x^6 + 2*x^7) / ((1 - x)^4*(1 + x)^2) + O(x^50)) \\ Colin Barker, Nov 14 2017
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Natan Arie Consigli, Jul 02 2016
STATUS
approved